Neil answer to Richard «about Newton's derivation of Kepler's laws of
planetary motion» pointed out the rationality of mechanics.
However, there is more on that:
In the book «Scientific Discovery, Computational explorations of the
creative process», Herbert Simon and coauthors develop a theory of rational
derivation of physical laws out of LOGIC and COMPUTER PROGRAMS. E. g.,
Kepler's laws are derived from computer experiments. I know that this
research program is now spread all over the world.
I always find out this as simple as extraordinary.
Another example, I always keep in mind is the logical-mathematical deduction
of the Friedmann's equations. A have now in my hands one little book called
«Cosmology» by Sir Herman Bondi. In the chapter on Newtonian cosmology, he
derives Friedmann's equations similarly as one does using General Relativity
(but with a different interpretation).
The universe is considered as a fluid. Then a general principal, the
cosmological principle, is stated. Then it comes: out of mathematics, by
pure logical thinking, Hubble's law is DERIVED (Hubble's law was first
proposed out of observations). Then Navier-Stokes equation is solved for the
Universe's fluid and Friedmann's equations come out of it. Navier-Stokes
equations used are of a particular kind where only the different
perspectives of Eulerian and Lagrangian velocities are indeed used, and
Newton's gravitation is represented by Poisson's equation. Then the chapter
concludes with rational power of the Newtonian system of reasoning about the
world starting with very few first principles.
Then we can speculate about axiomatics of Netonian mechanics: back from Elie
Cartan's workings in the 20ties to István Németi and co-authors works
nowadays.
J Felix
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J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel: 351 - 21 - 841 71 45
fax: 351 - 21 - 841 75 98
e-mail: fgc at math.ist.utl.pt
www: http://fgc.math.ist.utl.pt/jfc.htm
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